Soliton Management in Periodic Systems

Domain-wall dynamics in the Landau-Lifshitz magnet and the classical-quantum correspondence for spin transport

“…The phases η i (x, t) = i(k i x + ω i t) and k 0 = −3i, ω 0 = 0, and k ± = ±i and ω ± = k 2 ± − ε 2 are determined from the scattering data (15). The full classification of the soliton spectrum is postponed to [44].…”

“…The theory of exactly solvable partial differential equations [1][2][3][4], colloquially known as the theory of solitons [5], represents one of the cornerstones of theoretical and mathematical physics. While the technique has been traditionally used mostly as a theoretical framework to describe various nonlinear wave phenomena such as dispersive shock waves [6,7] and modulational instabilities [8][9][10], soliton systems also played an instrumental role in a broader range of physics applications, ranging from experimentally relevant setups with cold atoms and BECs [11], ocean waves [12], physics of plasmas and nonlinear media [13], Josephson junctions and nonlinear optics [14][15][16], and many theoretical concepts including the AdS/CFT correspondence [17,18], Gromov-Witten theory [19], Painlevé transcendents [20][21][22] and random matrix theory [23,24].…”

Non-autonomous Ginzburg-Landau solitons using the He-Li mapping method

“…Previously, some exact solutions were obtained by other methods. For example, the stability of chirped bright and dark soliton-like solutions of the cubic CGL equation with variable coefficients has been investigated in (Fang, & Xiao, 2006), but here we will use a modified He-Li mapping (He & Li, 2011;Pérez-Maldonado, & Rosu, 2015).…”

“…Nowadays, there are significant advances in the description of pulses in nonlinear media and the way they can be manipulated. The NLS equation with variable coefficients, and its non-autonomous nonlinear dynamical systems form (Malomed, 2006;He & Li, 2011;Pérez-Maldonado, & Rosu, 2015) are very important in this context of variable dispersion and nonlinearity, which bring losses and gains during the propagation. The manipulation of these pulses for optimal propagation is usually called "soliton management", or also for its specific use in optical devices as "dispersion management" (Malomed, 2006;Porsezian et al, 2007;Centurion et al, 2006).…”